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More results on degree deviation and degree variance | ||
| Journal of Mahani Mathematical Research | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 تیر 1404 اصل مقاله (527.78 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2025.24749.1757 | ||
| نویسندگان | ||
| Mohsen Sayadi1؛ Hasan Barzegar* 1؛ Saeid Alikhani2 | ||
| 1Department of Mathematics, Tafresh University, 39518-79611, Tafresh, Iran | ||
| 2Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran | ||
| چکیده | ||
| This paper investigates degree deviation and variance in graph theory, with a specific focus on $k$-regular graphs and subdivision of graphs. These metrics are fundamental for characterizing graph irregularity and have significant applications in network analysis and the social sciences. Furthermore, we introduce novel geometric measures of irregularity, geometric degree deviation and geometric degree variance derived from the geometric mean of vertex degrees. By means of rigorous theorems and illustrative examples, we explore the relationships between graph structures and their degree properties. Our findings seek to advance the current understanding of graph irregularity and provide a solid foundation for future research in this area. | ||
| کلیدواژه‌ها | ||
| Irregularity؛ Degree deviation؛ Degree variance | ||
| مراجع | ||
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[2] Albertson, M. O. (1997). The irregularity of a graph. Ars Combin, 46, 219-225.
[3] Alikhani, S., Ghanbari, N., & Soltani, S. (2023). Total dominator chromatic numbre of k-subdivision of graphs. Art Discrete Appl. Math, 6 #P1.10.
[4] Bell, F. K. (1992). A note on the irregularity of a graph. Linear Algebra and its Applications, 161, 45-54. https://doi.org/10.1016/0024-3795(92)90004-t.
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[6] Furtula, B., Gutman, I., Vukicevic, Z. K., Lekishvili, G., & Popivoda, G. (2015). On an old/new degreebased topological index. Bull. Acad. Serbe Sci. Arts (Cl. Sci. Math. Natur.), 40, 19-31.
[7] Ghalavand, A., Reti, T., Milovanovic, I. Z., & Ashra , A. R. (2022) Graph irregularity characterization with particular regard to bidegreed graphs. arXiv, DOI: arXiv:2211.06744. https://doi.org/10.48550/arXiv.2211.06744.
[8] Gutman, I. (2016). Irregularity of molecular graph. Kragujevac J. Sci., 38, 99-109. https://doi.org/10.5937/kgjsci1638071g. [9] Nikiforov, V. (2006). Eigenvalues and degree deviation in graph. Linear Alg. Appl., 414, 347-360. https://doi.org/10.1016/j.laa.2005.10.011.
[10] West, D. B. (2001). Introduction to graph theory. 2nd ed. , Prentice Hall.
[11] Sayadi, M., Barzegar, H., Alikhani, S., & Ghanbari, N. (2025, April). Bell's Degree Variance and Degree Deviation in Graphs: Analyzing Optimal Graph Based on These Irregularity Measures, Control and Optimization in Applied Mathematics, Available Online. https://doi.org/10.30473/coam.2025.73746.1288. | ||
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آمار تعداد مشاهده مقاله: 37 تعداد دریافت فایل اصل مقاله: 24 |
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